Stabilizing influence of axial momentum spread on the two-stream instability in intense heavy ion beams

This paper makes use of the Vlasov–Maxwell equations to describe the electron–ion two-stream instability driven by the directed axial motion of a high-intensity ion beam propagating through a stationary population of (unwanted) background electrons in the acceleration region or beam transport lines. The ion beam is treated as continuous in the z-direction, and the electrons are electrostatically confined in the transverse direction by the space-charge potential produced by the excess ion charge. The analysis is carried out for arbitrary beam intensity, consistent with transverse confinement of the beam particles, and arbitrary fractional charge neutralization by the background electrons. For the case of overlapping step-function ion and electron density profiles, corresponding to Kapchinskij–Vladimirskij (KV) electron and ion distributions in the transverse direction, detailed stability properties are calculated including parallel kinetic effects over a wide range of system parameters for dipole perturbations with azimuthal mode number ℓ=1. The instability growth rate is found to increase with increasing beam intensity, increasing fractional charge neutralization, and decreasing proximity of the conducting wall. For space-charge-dominated beams, it is shown that Landau damping associated with a modest axial momentum spread of the beam ions and background electrons has a strong stabilizing influence on the two-stream instability.